An efficient method for evaluating energy-dependent sum rules

Abstract

Energy-dependent sum rules are useful tools in many fields of physics. In nuclear physics, they typically involve an integration of the response function over the nuclear spectrum with a weight function composed of integer powers of the energy. More complicated weight functions are also encountered, e.g., in nuclear polarization corrections of atomic spectra. Using the Lorentz integral transform method and the Lanczos algorithm, we derive a computationally efficient technique for evaluating such sum rules that avoids the explicit calculation of both the continuum states and the response function itself. Our numerical results for electric dipole sum rules of the Helium-4 nucleus with various energy-dependent weights show rapid convergence with respect to the number of Lanczos steps. This demonstrates the usefulness of the method in a variety of electroweak reactions.

7 pages, 2 figures, 1 table

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Cited by in corpus (26)

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• Giant and pigmy dipole resonances in 4He, 16,22O, and 40Ca from chiral nucleon-nucleon interactions
• From bound states to the continuum
• Electric dipole polarizability from first principles calculations
• Optical potentials for the rare-isotope beam era
• Nuclear structure effects in light muonic atoms
• Improved estimates of the nuclear structure corrections in $\mu$D
• Ab initio calculation of nuclear structure corrections in muonic atoms
• Nuclear structure corrections to the Lamb shift in ${\mu }^3$He${}^{+}$ and ${\mu }^3$H
• Benchmark calculations of electromagnetic sum rules with a symmetry-adapted basis and hyperspherical harmonics
• Charge and Magnetic Properties of Three-Nucleon Systems in Pionless Effective Field Theory
• Zemach moments and radii of 2,3H and 3,4He
• Complex-energy approach to sum rules within nuclear density functional theory
• Probing uncertainties of nuclear structure corrections in light muonic atoms
• Transition sum rules in the shell model
• Update on nuclear structure effects in light muonic atoms
• Revisiting the helium isotope-shift puzzle with improved uncertainties from nuclear structure corrections
• Electric dipole polarizability of ${}^{58}$Ni
• Basis Light-Front Quantization for a Chiral Nucleon-Pion Lagrangian
• Exact sum rules with approximate ground states
• Understanding the proton radius puzzle: Nuclear structure effects in light muonic atoms
• Sub Coulomb barrier d+${}^{208}$Pb scattering in the time-dependent basis function approach
• Direct ab initio calculation of the ${}^4$He nuclear electric dipole polarizability
• Electromagnetic Excitations and Responses in Nuclei from First Principles
• Electric dipole polarizability: from few- to many-body systems
• Systematic analysis of double Gamow-Teller sum rules